Abstract:
In this paper we consider the set of quantum states and passages to the limit for sequences of quantum dynamic semigroups in the mentioned set. We study the structure of the set of extreme points of the set of quantum states and represent an arbitrary state as an integral over the set of one-dimensional orthogonal projectors; the obtained representation is similar to the spectral decomposition of the normal state. We apply the obtained results to the analysis of the limit behavior of sequences of quantum dynamic semigroups which occur in the regularization of the degenerate Hamiltonian.
Citation:
V. Z. Sakbaev, “The set of quantum states and its averaged dynamic transformations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 10, 48–58; Russian Math. (Iz. VUZ), 55:10 (2011), 41–50
\Bibitem{Sak11}
\by V.~Z.~Sakbaev
\paper The set of quantum states and its averaged dynamic transformations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 10
\pages 48--58
\mathnet{http://mi.mathnet.ru/ivm8101}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2918336}
\elib{https://elibrary.ru/item.asp?id=16546274}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 10
\pages 41--50
\crossref{https://doi.org/10.3103/S1066369X11100069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856271379}
Linking options:
https://www.mathnet.ru/eng/ivm8101
https://www.mathnet.ru/eng/ivm/y2011/i10/p48
This publication is cited in the following 7 articles:
Efremova L.S., Grekhneva A.D., Sakbaev V.Zh., “Phase Flows Generated By Cauchy Problem For Nonlinear Schrodinger Equation and Dynamical Mappings of Quantum States”, Lobachevskii J. Math., 40:10, SI (2019), 1455–1469
I. V. Volovich, V. Zh. Sakbaev, “On quantum dynamics on C∗-algebras”, Proc. Steklov Inst. Math., 301 (2018), 25–38
G. G. Amosov, V. Zh. Sakbaev, “Geometric properties of systems of vector states and expansion of states in Pettis integrals”, St. Petersburg Math. J., 27:4 (2016), 589–597
G. G. Amosov, V. Zh. Sakbaev, “On Analogs of Spectral Decomposition of a Quantum State”, Math. Notes, 93:3 (2013), 351–359
V. Sakbaev, “On dynamical properties of a one-parameter family of transformations arising in averaging of semigroups”, Journal of Mathematical Sciences, 202:6 (2014), 869–886
V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459
Amosov G.G., Sakbaev V.Zh., Smolyanov O.G., “Linear and Nonlinear Liftings of States of Quantum Systems”, Russ. J. Math. Phys., 19:4 (2012), 417–427
Citation in format AMSBIB
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